Spatial Survey Data Modeling - Sampling Spatial Units for Agricultural Surveys - page 320

1 p k , p k ¼

p k

where logit pðÞ¼ , and y k is binary (i.e., can only

assume the values 0 or 1). Logistic regression models for sample data are also
fitted using svyglm.
See Lumley ( 2010 , Chap. 6) for an empirical review of methods for categorical
sample data.
It is not trivial to extend these methods to spatially distributed data. This represents
a new challenge for survey researchers. In particular, research is needed to derive
more appropriate procedures for estimating spatial models. Obviously, it is also
evident that standard regression analysis should be modified to take into account
spatial effects. These are some research ideas that we aim to exploit in the near future.

log Pr y k ¼ ð 1 Þ

Conclusions
The matters outlined in this chapter are very remarkable in the field of survey
sampling. However, the predictive approach and the analysis of survey data
are two topics that have only attracted a small amount of attention when
compared with the traditional approach of sampling from a finite population.
This last approach has been extensively analyzed in the rest of this topic.
The main aim of this chapter is to properly emphasize these two different
and important topics that are generally based on modeling assumptions.
Furthermore, spatial effects that are very important features in agricultural
surveys are often neglected in the predictive approach to sampling, and in the
analysis of survey data. The inclusion of spatial information could represent a
very important challenge to be addressed by researchers in the near future.
We have tried to highlight the basic ideas for these arguments and raise some
research questions, and to develop a unified approach for geographically
distributed data.
However, the main problem is that many analysts do not consider sampling
as a crucial issue in regional science research. In fact, this subject has not been
extensively analyzed by regional scientists and practitioners. Most reference
topics do not address this issue, and those that do only include marginal
discussions. The only exception is Haining ( 2003 ) that includes a paragraph
(see p. 93 and following) describing the problem of spatial sampling. However,
regional scientists have recently had a renewed interest in spatial sampling. In
fact, the Handbook of Regional Science (Fischer and Nijkamp 2013 )containsa
chapter entirely devoted to this concern (Delmelle 2013 ). This chapter demon-
strates the particular importance of spatial sampling in regional science, but
describes only a small section of the available spatial sampling methods.
The aim of this topic has been to fill this gap in the literature. Furthermore,
with this work we would like to indicate a possible connection between
quantitative geographers and statisticians, which may hopefully lead to dra-
matic developments in the theory and integration of sampling surveys and
spatially distributed data. We will leave it to the careful reader to decide if our
demanding objective has been achieved.